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daemonturk
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 A High School level Problem (Interesting)   « on: Jul 27th, 2009, 3:47am » Quote Modify

A straight track on a hillside makes an angle of 50 degrees with the line of greatest slope and an angle of 11 degree 28 minutes with the horizontal. Find the angle the hillside makes with the horizontal.

Cookies goes to the shortest and simplest solution.
 « Last Edit: Jul 27th, 2009, 3:47am by daemonturk » IP Logged
Grimbal
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 Re: A High School level Problem (Interesting)   « Reply #1 on: Jul 27th, 2009, 4:24am » Quote Modify

Are the 50° measured horizontally (as on a map) or in 3D?
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daemonturk
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 Re: A High School level Problem (Interesting)   « Reply #2 on: Jul 27th, 2009, 8:51am » Quote Modify

For that particular angle, 3D.
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Grimbal
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 Re: A High School level Problem (Interesting)   « Reply #3 on: Jul 27th, 2009, 9:13am » Quote Modify

18°?
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daemonturk
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 Re: A High School level Problem (Interesting)   « Reply #4 on: Jul 27th, 2009, 9:21am » Quote Modify

Correct. But working?
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Grimbal
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 Re: A High School level Problem (Interesting)   « Reply #5 on: Jul 27th, 2009, 9:35am » Quote Modify

Let's call alpha = 11°28, beta = 50°, and gamma the hill slope.

If we take a unit length l of track and call h is the altitude difference, then
h = l·sin(alfa)

On the other side, if d is the distance along the greatest slope that has the same difference, we have
d = l·cos(beta)
and
h = d·sin(gamma)

All this together gives
sin(gamma) = h/d = sin(alfa)/cos(beta).

It would be clearer with a picture that shows where the right angles are.
 « Last Edit: Jul 27th, 2009, 9:36am by Grimbal » IP Logged
daemonturk
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 Re: A High School level Problem (Interesting)   « Reply #6 on: Sep 1st, 2009, 4:21am » Quote Modify

Ya.
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